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$$\underset{b \in C^\infty_{cp}(\Sigma)}{\forall} \left( d \mathcal{S}_{b \mathbf{L}}(\Phi) = 0 \right) \;\Leftrightarrow\; \left( j^\infty_\Sigma(\Phi)^\ast ( \delta_{EL} \mathbf{L} ) = 0 \right) \,.$$